An optimal investment problem is investigated under inflation risk and incentive schemes. Consider a continuous-time model of a financial market with inflation risk. Suppose that the financial market consists of three tradable assets: an index bond, a stock and a risk-free bond. The asset manager is remunerated through a scheme based on the performance of the fund with respect to a benchmark. A remuneration scheme is designed as a nonlinear function of the relative performance. The concavification technique and the martingale approach are applied to solve the optimization problem and the closed-form representations of the optimal relative performance and portfolio processes under two different remuneration schemes are derived. Furthermore, sensitivity analysis is presented to analyze the impacts of the two different incentive schemes and inflation risk on the optimal investment strategy of the asset manager. Numerical results reveal that inflation-indexed bonds can effectively help investors to hedge against inflation risk, and the call-put option compensation scheme can improve the risk management in bad economic states.